Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential

Driven particle in a two-dimensional periodic substrate: Nonmonotonic dependence of drift velocity on temperature

Motion of a driven particle in a two-dimensional (2D) periodic potential of square symmetry is studied by means of Brownian dynamics simulations. The average drift velocity and long time diffusion coefficients are obtained as a function of driving force and temperature. For driving forces above the critical depinning force, a reduction of drift velocity is observed as temperature is increased. The drift velocity reaches a minimum for temperatures at which k_{B}T is of the order of the barrier height of the substrate potential and then increases and saturates to the value of drift velocity for the substrate free case. Depending on the driving force, the drop in drift velocity can be as large as 36% of its value at low temperatures. While this phenomenon is observed in 2D for different types of substrate potentials studied and for various drive directions, studies using the exact result show no such dip in drift velocity in one dimension (1D). As in the case of 1D, a peak is observed in the longitudinal diffusion coefficient as the driving force is varied at a fixed temperature. But unlike in 1D, the location of the peak is temperature dependent. Approximate analytical expressions for the average drift velocity and the longitudinal diffusion coefficient are formulated using the exact results in 1D by finding a temperature dependent effective 1D potential to model the motion in the presence of a 2D substrate. This approximate analysis is successful in qualitatively predicting the observations.

Lane and band formation of oppositely driven colloidal particles in two-dimensional ring geometries

We study the segregation phenomena for oppositely driven colloidal particles in two-dimensional ring geometries by means of Brownian dynamics simulations without hydrodynamic interactions. The particles interact via a repulsive Yukawa potential and are confined to a two-dimensional circular channel by hard walls, in which half of the particles are driven clockwise and the other half are driven counterclockwise. In addition to lane formation, which is commonly found in oppositely driven systems, we found band formation along the angular direction in channels with a very large radius. This indicates that a formation of lanes is prevented in the limit of channels with an infinitely large inner radius. The dependency of this segregation has been examined for the two control parameters, the interaction strength between the particles and the width of the circular channel.

Group formation and collective motion of colloidal rods with an activity triggered by visual perception

We investigate the formation of cohesive groups and the collective diffusion of colloidal spherocylinders with a motility driven by a simple visual perception model. For this, we perform Brownian dynamics simulations without hydrodynamic interactions. The visual perception is based on sight cones attached to the spherocylinders and perception functions quantifying the visual stimuli. If the perception function of a particle reaches a predefined threshold, an active component is added to its motion. We find that, in addition to the opening angle of the cone of sight, the aspect ratio of the particles plays an important role for the formation of cohesive groups. If the elongation of the particles is increased, the maximum angle for which the rods organize themselves into such groups decreases distinctly. After a system forms a cohesive group, it performs a diffusive motion, which can be quantified by an effective diffusion coefficient. For increasing aspect ratios, the spatial expansion of the cohesive groups and the effective diffusion coefficient of the collective motion increase, while the number of active group members decreases. We also find that a larger particle number, a smaller propulsion velocity of the group members, and a smaller threshold for the visual stimulus increase the maximum opening angle for which cohesive groups form. Based on our results, we expect anisotropic particles to be of great relevance for the adjustability of visual perception-dependent motility.

Microscopic diffusion coefficients of dumbbell- and spherocylinder-shaped colloids and their application in simulations of crowded monolayers

We explore the diffusion properties of colloidal particles with dumbbell and spherocylinder shapes using a hydrodynamic bead-shell approach and additional Brownian dynamics (BD) simulations. By applying the bead-shell method, we determine empirical formulas for the microscopic diffusion coefficients. A comparison of these formulas and established experimental and theoretical results shows remarkable agreement. For example, the maximum relative discrepancy found for dumbbells is less than 5%. As an application example of the empirical formulas, we perform two-dimensional (2D) BD simulations based on a single dumbbell or spherocylinder in a suspension of spheres and calculate the resulting effective long-time diffusion coefficients. The performed BD simulations can be compared to quasi-2D systems such as colloids confined at the interface of two fluids. We find that the effective diffusion coefficient of translation mostly depends on the sphere area fraction ϕ, while the effective diffusion coefficient of rotation is influenced by the aspect ratio and ϕ. Furthermore, the effective rotational diffusion constant seems to depend on the particle shape with the corresponding implementation of the interactions. In the resolution limit of our methods, the shape-dependent differences of the microscopic diffusion coefficients and the long-time diffusion constant of translation are negligible in the first approximation. The determined empirical formulas for the microscopic diffusion coefficients add to the knowledge of the diffusion of anisotropic particles, and they can be used in countless future studies.

Phase behaviour in 2D assemblies of dumbbell-shaped colloids generated under geometrical confinement

The structure formation and the phase behaviour of monolayers of dumbbell-shaped colloids are explored. For this, we conduct Langmuir-Blodgett experiments at the air/water interface and conventional Brownian dynamic simulations without hydrodynamic interactions. Using Voronoi tessellations and the probability density of the corresponding shape factor of the Voronoi cells p(ζ), the influence of the area fraction φ on the structure of the monolayers is investigated. An increase of the area fraction leads to a higher percentage of domains containing particles with six nearest neighbours and a sharper progression of p(ζ). Especially in dense systems, these domains can consist of aligned particles with uniform Voronoi cells. Thus, the increase of φ enhances the order of the monolayers. Simulations show that a sufficient enhancement of φ also impacts the pair correlation function which develops a substructure in its first maxima. Furthermore, we find that reducing the barrier speed in the Langmuir-Blodgett experiments enhances the final area fraction for a given target surface pressure which, in turn, also increases the percentage of particles with six nearest neighbours and sharpens the progression of p(ζ). Overall, the experiments and simulations show a remarkable qualitative agreement which indicates a versatile way of characterising colloidal monolayers by Brownian dynamics simulations. This opens up perspectives for application to a broad range of nanoparticle-based thin film coatings and devices.

Negative resistance for colloids driven over two barriers in a microchannel

When considering the flow of currents through obstacles, one core expectation is that the total resistance of sequential single resistors is additive. While this rule is most commonly applied to electronic circuits, it also applies to other transport phenomena such as the flow of colloids or nanoparticles through channels containing multiple obstacles, as long as these obstacles are sufficiently far apart. Here we explore the breakdown of this additivity for fluids of repulsive colloids driven over two energetic barriers in a microchannel, using real-space microscopy experiments, particle-resolved simulations, and dynamical density functional theory. If the barrier separation is comparable to the particle correlation length, the resistance is highly non-additive, such that the resistance added by the second barrier can be significantly higher or lower than that of the first. Surprisingly, in some cases the second barrier can even add a negative resistance, such that two identical barriers are easier to cross than a single one. We explain this counterintuitive observation in terms of the structuring of particles trapped between the barriers.

Energy landscape of colloidal dumbbells in a periodic distribution of light

Using a ray tracing calculation, the energy landscape of dumbbells, made of spherical colloidal particles, interacting with a periodic distribution of light is calculated. As shown previously [E. Sarmiento-Gomez, J. A. Rivera-Moran and J. L. Aruaz-Lara, Soft Matter, 2018, 14, 3684], planar aggregates of spherical particles adopt discrete configurations in such light distribution. Here we focus on the case of colloidal dumbbells both symmetric and asymmetric from an experimental and theoretical point of view. It has been shown that the direct calculation using the ray tracing approximation is in excellent agreement with the experiment in spite of the fact that the particles size and the wavelength of the trapping light are comparable. We also corroborate, at least for the more simple case of a single particle in a parabolic light distribution, that the simple method used here provides the same results as the more complex and general Lorenz-Mie approach giving a more simple yet reliable method for the calculation of the energy landscape of colloidal aggregates in periodic light distributions.

Dynamic ordering of driven spherocylinders in a nonequilibrium suspension of small colloidal spheres

The ordering effects of driven spherocylinder-shaped rods in a colloidal suspension of small spheres confined to a two-dimensional channel geometry are observed via Brownian dynamics simulations without hydrodynamics. To describe the ordering, an order parameter and an expression for a potential of mean force of an equivalent equilibrium system are defined and analyzed. By varying the application point of the external force along the rods and thus the resulting lever, a transition from a preferred orientation parallel to the direction of the force to a preferred orientation perpendicular to the direction of the force was observed. It is shown that this effect can only be found if the spheres and multiple rods are present. Furthermore, a dependency of the order parameter on the absolute value of the force was discovered. The analysis of the potential of mean force further indicates a transition between two different phases of mean orientation. An observation of the flow equilibrium mean velocity in channel direction led to a s-shaped progression regarding the lever dependency, also marking a transition between two states linked to the mean orientation of the rods. A finite size analysis was conducted. Its results indicate that the transition between the two orientation states is a general phenomenon of the observed rod-sphere mixture.

Depinning and heterogeneous dynamics of colloidal crystal layers under shear flow

Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange in well-defined layers with solidlike in-plane structure, the confined films display complex, nonlinear behavior such as collective depinning and local transport via density excitations. These phenomena are reminiscent of colloidal monolayers driven over a periodic substrate potential. In order to deepen this connection, we present an effective model that maps the dynamics of the shear-driven colloidal layers to the motion of a single particle driven over an effective substrate potential. This model allows us to estimate the critical shear rate of the depinning transition based on the equilibrium configuration, revealing the impact of important parameters, such as the slit-pore width and the interaction strength. We then turn to heterogeneous systems where a layer of small colloids is sheared with respect to bottom layers of large particles. For these incommensurate systems we find that the particle transport is dominated by density excitations resembling the so-called "kink" solutions of the Frenkel-Kontorova (FK) model. In contrast to the FK model, however, the corresponding "antikinks" do not move.

Development of 3-dimensional time-dependent density functional theory and its application to gas diffusion in nanoporous materials

An entropy scaling based TDDFT has been proposed and applied to diffusion in a nanoporous material.

Understanding the approximations of mode-coupling theory for sheared steady states of colloids

The lack of clarity of various mode-coupling theory (MCT) approximations, even in equilibrium, makes it hard to understand the relation between various MCT approaches for sheared steady states as well as their regime of validity. Here we try to understand these approximations indirectly by deriving the MCT equations through two different approaches for a colloidal system under shear, first through a microscopic approach, as suggested by Zaccarelli et al., and second through fluctuating hydrodynamics, where the approximations used in the derivation are quite clear. The qualitative similarity of our theory with a number of existing theories show that linear response theory might play a role in various approximations employed in deriving those theories and one needs to be careful while applying them for systems arbitrarily far away from equilibrium, such as a granular system or when shear is very strong. As a by-product of our calculation, we obtain the extension of the Yvon-Born-Green (YBG) equation for a sheared system and under the assumption of random-phase approximation, the YBG equation yields the distorted structure factor that was earlier obtained through different approaches.

Segregation of oppositely driven colloidal particles in hard-walled channels: A finite-size study

We investigate segregation phenomena of particles driven in opposite directions with Brownian dynamics simulations. The particles interact via a repulsive potential and are confined in three-dimensional hard-walled pipes with quadratic cross sections. In a systematic finite-size study, the pipe length is varied. Ordering on finite length scales can be observed, but global segregation seems to vanish for infinite channel length, as it was recently found for lane formation in two dimensions. As an additional effect of the finite hard-walled boundary conditions, interface vibrations and longitudinal demixing are found.